Evaluation of pairwise distances among points forming a regular orthogonal grid in a hypercube

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26110%2F18%3APU129085" target="_blank" >RIV/00216305:26110/18:PU129085 - isvavai.cz</a>

Výsledek na webu

<a href="https://journals.vgtu.lt/index.php/JCEM/article/view/5189" target="_blank" >https://journals.vgtu.lt/index.php/JCEM/article/view/5189</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3846/jcem.2018.5189" target="_blank" >10.3846/jcem.2018.5189</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Evaluation of pairwise distances among points forming a regular orthogonal grid in a hypercube

Popis výsledku v původním jazyce

Cartesian grid is a basic arrangement of points that form a regular orthogonal grid (ROG). In some applications, it is needed to evaluate all pairwise distances among ROG points. This paper focuses on ROG discretization of a unit hypercube of arbitrary dimension. A method for the fast enumeration of all pairwise distances and their counts for a high number of points arranged into high-dimensional ROG is presented. The proposed method exploits the regular and collapsible pattern of ROG to reduce the number of evaluated distances. The number of unique distances is identified and frequencies are determined using combinatorial rules. The measured computational speed-up compared to a naïve approach corresponds to the presented theoretical analysis. The proposed method and algorithm may find applications in various fields. The paper shows application focused on the behaviour of various distance measures with the motivation to find the lower bounds on the criteria of point distribution uniformity in Monte Carlo integration.

Název v anglickém jazyce

Evaluation of pairwise distances among points forming a regular orthogonal grid in a hypercube

Popis výsledku anglicky

Cartesian grid is a basic arrangement of points that form a regular orthogonal grid (ROG). In some applications, it is needed to evaluate all pairwise distances among ROG points. This paper focuses on ROG discretization of a unit hypercube of arbitrary dimension. A method for the fast enumeration of all pairwise distances and their counts for a high number of points arranged into high-dimensional ROG is presented. The proposed method exploits the regular and collapsible pattern of ROG to reduce the number of evaluated distances. The number of unique distances is identified and frequencies are determined using combinatorial rules. The measured computational speed-up compared to a naïve approach corresponds to the presented theoretical analysis. The proposed method and algorithm may find applications in various fields. The paper shows application focused on the behaviour of various distance measures with the motivation to find the lower bounds on the criteria of point distribution uniformity in Monte Carlo integration.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of civil engineering and management

ISSN

1392-3730

e-ISSN

1822-3605

Svazek periodika

24

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

LT - Litevská republika

Počet stran výsledku

14

Strana od-do

410-423

Kód UT WoS článku

000446022400005

EID výsledku v databázi Scopus

—